EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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Question
Chapter 3.4, Problem 39E
To determine
To find : solution to the exponential equation algebraically.
Expert Solution & Answer
Answer to Problem 39E
The solution to the equation 4x=5x2 is x=0 & x≈0.861 _
Explanation of Solution
Given information: 4x=5x2
Concept Involved:
The word “solve” means the process of finding the value of x that makes the equation true. In order to solve we need to undo whatever is done to x .
Formula Used
lnmn=n(lnm)
lne=1
Calculation:
Take natural logarithm on both sides of the equation
ln4x=ln5x2
Use the logarithmic property lnmn=n(lnm) on both sides of the equation to rewrite it
x⋅ln4=x2⋅ln5
Subtracting x⋅ln4 on both sides of the equation in order to get x alone in one side of the equation
x⋅ln4−x⋅ln4=x2⋅ln5−x⋅ln4
Simplify on both sides of the equation
0=x2⋅ln5−x⋅ln4
Use symmetric property of equality to rewrite the equation
x2⋅ln5−x⋅ln4=0
Factor x in left side of the equation
x(x⋅ln5−ln4)=0
Use the zero factor property which states that “if ab=0 , then a=0 or b=0 ” to set each factor equal to 0
x=0 ►1st equation
x⋅ln5−ln4=0 ►2nd equation
Solve the 2nd equation x⋅ln5−ln4=0
- By adding ln4 on both sides, then
- By Simplifying on both sides of the equation, then
- By dividing ln5 on both sides, and then
- By Simplifying fraction on both sides
x⋅ln5−ln4+ln4=0+ln4
x⋅ln5=ln4
x⋅ln5ln5=ln4ln5
x=ln4ln5
x≈0.861
Check for extraneous solution by substituting the result in the original equation.
Both x=0 & x≈0.861 makes the original equation TRUE
Conclusion:
The solution to the equation 4x=5x2 is x=0 & x≈0.861 _
Chapter 3 Solutions
EBK PRECALCULUS W/LIMITS
Ch. 3.1 - Prob. 1ECh. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10E
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Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning
Implicit Differentiation with Transcendental Functions; Author: Mathispower4u;https://www.youtube.com/watch?v=16WoO59R88w;License: Standard YouTube License, CC-BY
How to determine the difference between an algebraic and transcendental expression; Author: Study Force;https://www.youtube.com/watch?v=xRht10w7ZOE;License: Standard YouTube License, CC-BY